Boundary Singularities in Linear Elliptic Differential Equations

Finite-difference methods are relatively inefficient in theneighbourhood of boundary singularities in elliptic problems.A combination of special treatment near the singularity, basedon local satisfaction of the differential equation and boundaryconditions, is here matched with finite-difference formulaein the rest of the field. The method is applied to a generalself-adjoint equation with either Dirichlet, Neumann or mixedconditions on parts of the boundary consisting of two straightlines meeting at the singular point. A practical problem, formerlysolved by more extensive labour, illustrates the power of themethod.